1. Field of the Invention
The present invention relates to techniques for automatically predicting a transition of up to several hours (or a short time) ahead of a precipitation region included in a narrow region which is sensitively affected by changes in the weather, and relates to methods and apparatus for predicting changes of a precipitation region as a non-rigid object, such as growth or dispersion.
This application is based on Japanese Patent Applications Nos. Hei 8-347684, Hei 9-29126, Hei 9-29127, Hei 9-29128, Hei 9-64665, Hei 9-99053, and Hei 9-183986, the contents of which are incorporated herein by reference.
2. Description of the Related Art
In conventional weather forecasting performed by, for example, the Japanese Meteorological Agency, transitions of meteorological phenomena of dozens of hours in advance or a few days in advance for each area in Japan are predicted via mathematical/physical equations using various two- or three-dimensional physical parameters (e.g., temperature, atmosphere, dew point, wind vector) which are obtained by the satellite Amedas or another meteorological satellite. Currently, shorter time-range weather forecasting on the order of minutes for a narrower region has been desired, and thus forecasting based on information of changes of a precipitation region (where rainfall or snowfall is generated), which is obtained via locally-arranged meteorological radar apparatus, has become important. Such forecasting is called "nowcasting", and changes of meteorological phenomena are observed so as to prevent disasters beforehand.
The meteorological radar emits pulses to a precipitation region in the sky a few kilometers above the ground so as to observe the strength of rainfall or snowfall according to reflective (or echo) intensities of the pulses (the intensities being converted into gray levels in the image). The precipitation region has apparently a cloud-like shape. An image of the precipitation region is represented as a combination pattern of various shapes and gray-levels (such a pattern will be called a "precipitation pattern", hereinafter). The reflection region is normally within a radius of a hundred kilometers. In most echo images, a conversion is performed in order that the amount of precipitation and the displayed gradation level are proportionate to each other, and the precipitation region corresponds to a part having the gradation levels (called "gray-levels", hereinafter) higher than a specified level.
Information on the precipitation pattern is updated every few minutes, and this feature is useful, for example, for scheduling departure/arrival of space shuttles or airplanes, or for preventing flood damage beforehand. However, it is difficult to represent clear feature quantities with respect to a precipitation pattern; thus, automatic prediction of a precipitation region based on image processing methods is also difficult. In most cases of conventional evaluation of moving vectors with respect to a rigid object included in an image, a model, on which illumination effects almost equally act for each part, is adopted. Conventional methods for detecting the moving vectors are mainly based on the Cross Correlation method (i.e., the CC method) (refer to D. H. Ballard, et al., "Computer Vision" Prentice-Hall, Inc.)
On the other hand, a follow-up method necessary for automatic prediction of a non-rigid object such as a precipitation pattern should be different from a method for following movement of a rigid object such as a motorcar, etc., or an elastic body observed in an echo image of the heart, or the like, and should make it possible to follow transition of the non-rigid object with detecting generation or disappearance of a pattern corresponding to the object. As for these demands, predicted results satisfying a desirable accuracy cannot be obtained in practice. Therefore, even now, manual and subjective detection according to transition of the precipitation region, based on experience of humans, is performed, and detected information is used in practice.
In the meantime, automatic and objective prediction methods for transition of a precipitation region using computers have been tested.
Representative precipitation patterns are (i) cyclonic disturbance generated within a radius of ten or hundred kilometers (called "meso-.beta. scale") and topographical ascending current (called "meso-.gamma. scale") observed at mountains. These phenomena are also characterized by having a short life of several minutes or hours. Accordingly, in order to precisely predict the phenomena of meso-.beta./.gamma. scale, a model which can represent an ever-changing narrow region within a radius of kilometers, where generation or disappearance of a pattern is observed, is required.
Until now, methods using image processing techniques and using physical equations have been proposed as such a precipitation pattern prediction method.
In the simplest method using image processing techniques, two consecutive images are subjected to pattern matching based on the CC method so as to evaluate moving vector(s), and by using a one-dimensional extrapolation method, a precipitation pattern (of the same shape and size) is translated. Here, displacement (of a precipitation pattern for the evaluation) per frame is regarded as a wind speed in a horizontal direction.
More specifically, regarding two (image) frames f(t) and f(t+1), which are functions at time (t) (at each step), a correlation value (or a correlation coefficient) is calculated so as to evaluate similarity of the gray-levels between these frames, and displacement of the relevant precipitation region is evaluated on the assumption that points having the highest correlation values in the frames correspond to each other. Then, based on the evaluated displacement, translation movement of the precipitation region is performed. By repeating the above operations using an image of the precipitation region of the next step obtained by the above evaluation, it is possible to predict precipitation-region images belonging to a specified number of steps ahead. That is, according to a two-dimensional image at a time, changes of several minutes or hours ahead of the precipitation region is predicted also as a two-dimensional image.
In the CC method applied to practical use, one moving vector is assumed from two consecutive images. Generally, generation/disappearance phenomena constantly occur in a precipitation region. Therefore, regarding the gray-level of images, gray-levels of a prior frame and the next frame are not always in one-to-one correspondence. Additionally, in a diffuse precipitation-region image for which the correlation coefficient cannot be evaluated, assumption of moving (i.e., advection) vectors is difficult and a suitable interpolation method for such a region has not previously been proposed.
Furthermore, in the prediction process according to the two-dimensional images as described above, the identical pattern is simply translated; thus, only spread of the precipitation region is predicted but degree of a change in the state of the precipitation region is not predicted. That is, unstable changes regarding size, shape, gray-level, and the like, which represent the natural phenomena, cannot be sufficiently predicted, and topographical influences on the precipitation region are also not considered. Accordingly, regarding the two-dimensional information as images, a series of physical phases of source, sink, dispersion, growth, and decay have not been represented.
For example, in the case of a stationary precipitation region, the growth and disappearance are violent in comparison with overall displacement of the precipitation region. That is, the gray-levels of such a precipitation region considerably change in comparison with the change of its contour shape. Therefore, if the above CC method is directly applied to such a precipitation region, multiple (unsuitable) moving vectors may be obtained because the gray-levels may be changed even if the entire pattern has not moved. As a result of moving the precipitation region based on the obtained (unsuitable) moving vectors, the predicted precipitation region becomes more and more out of place as the prediction proceeds.
Similarly, prediction in consideration of increasing/decreasing process relating to the precipitation area, which relates to the amount of precipitation, is also not realized. Therefore, if prediction is continued using a precipitation pattern in the growing phase, the size of the precipitation pattern does not become small even though the actual phase enters a decaying phase. Conversely, even though the actual phase proceeds from the decaying phase to a growing phase again, the size of the precipitation pattern does not become large and consequently, prediction error increases at a remarkable switching phase between the above phases. That is, in the conventional linear prediction method, a non-linear change of the area cannot be predicted before and after the status of the area change of a precipitation region shifts from increase to decrease, or from decrease to increase. Consequently, there has been a problem in that increase of the prediction error is inevitable.
That is, it can be said that moving vectors suitable for meteorological patterns which non-rigidly change cannot be defined. This is because even between consecutive images, plural attributes of contour, gray-level, and the like of the object simultaneously change, thus clear correspondence between the images cannot be defined. Accordingly, by using the above automatic method, it is still difficult to define detailed correspondence between precipitation patterns of the frames, and evaluation of moving (i.e., advection) velocities with respect to precipitation patterns based on human experience is mainly used in practice.
On the other hand, if various advection vectors exist ini a precipitation pattern, a subblock matching method (in which a frame is divided into plural blocks) based on the CC method and the linear extrapolation method are used together. Regarding the accuracy of the moving vectors evaluated using the subblock matching method, it has been reported that the error between the moving vectors (of the subblock matching method) and moving vectors detected using the Doppler radar is small.
The reasons for adopting the CC method are (1) statistical estimation is effective because in most cases, definition of clear correspondence between frames is difficult due to the generation and disappearance phenomena, (2) large sampling interval (or period) can be adopted, etc.
In the meantime, the following are incapabilities of the (CC method: (1) if gray-levels in a precipitation pattern are distributed over a wide range, a reliable correlation coefficient cannot be obtained, (2) even though an image is divided into plural blocks using the subblock matching method, moving vectors for each pixel cannot be evaluated, and (3) displacement of concave/convex parts in the contour cannot be detected.
On the other hand, if the precipitation pattern is moved only by using the linear extrapolation method, the following problems occur: (1) the precipitation pattern unnaturally moves out of the image frame, (2) evaluated moving vectors cross each other, etc. Therefore, only by performing linear and translation movement of the precipitation pattern, improvement of the prediction accuracy has its limit.
Additionally, when the CC method and the linear extrapolation methods are used together, a simple model based on the assumption that the change of the precipitation region has been fixed (the gray-levels and the contour shape are not changed). That is, a non-physical prediction model against ever-changing meteorological phenomena has been used. Furthermore, insufficient statistical information has been known with respect to temporary growth of a precipitation region observed in its decaying phase, and thus prediction for such a condition has not been tried.
On the other hand, as an example of using a physical model, those using a diffusion equation or an advection equation have been reported. In the method reported in Y Asuma, et al., "Experiments for a Very-short-range Prediction of Snowfall Using a Simple Weather Radar System Part 2. --Examples of Actual Prediction--, Geographical Bulletin of Hokkaido University, Vol. 44, pp. 53-65, October, 1984", the diffusion equation and the CC method are used together, where the diffusion coefficient in the equation is fixed regardless of characteristics of a precipitation pattern. There has been a problem in that if this diffusion coefficient is not appropriately determined, obtained diffusivity tends to be larger than the actual. Here, transition of precipitation of a precipitation pattern is obtained as a solution of the diffusion equation and the entire precipitation pattern is uniformly translated by using the CC and linear extrapolation methods. Accordingly, there remain problems in that processes for objectively determining diffusion coefficients suitable for various precipitation patterns have not yet been found, and such a simple linear extrapolation method is directly used in the prediction.
Furthermore, two-dimensional images as sections of three-dimensional phenomena are analyzed; thus, it has been unnatural to represent such a three-dimensional physical diffusion phenomenon by using the diffusion equation. Additionally, the diffusion equation has scarcely been applied to a disappearance phase.
On the other hand, in T. Takasao et al., "SHORT-TERM RAINFALL PREDICTION BY A RADAR RAINGAUGE", Annual Report of Disaster Prevention Research Inst., Kyoto University, Vol. 26 B-2, pp. 165-180, April, 1983, growth and decaying terms are considered and defined in an advection equation, and a linear prediction equation, approximated by a linear function with a variable of precipitation intensity, is used on the assumption that a solution of the equation exists on the relevant basic characteristic curve. In this case, the moving velocity is evaluated based on the CC method.
In this method, a region to be analyzed is divided to be a mesh form, and parameters used in the linear function are independently determined for each section in the mesh. In this way, local changes are also considered. However, a simplified linear prediction equation is used on the assumption that changes of the precipitation intensity in each section (of the mesh) are insignificant; thus, application of this method to a precipitation pattern with a high changing rate of precipitation intensity is questionable. According to such simplification of the equation, effects caused by the growth and decay terms are not explicitly reflected to predicted results.
As described above, the prediction methods based on the CC and linear extrapolation methods or the simplified physical equation are convenient but similar to the method for predicting movement of a rigid object. Therefore, the model in this case cannot flexibly applied to:
(1) a precipitation pattern like rapidly growing and expanding in a short time, as those found in the meso-.beta./.gamma. scale, PA0 (2) a case in which the precipitation intensity is locally changed in accordance with a growing or decaying phase, or PA0 (3) non-linear movement of a precipitation pattern. PA0 (1) systematically represent a series of physical processes in a precipitation region, PA0 (2) perform prediction by accurately evaluating moving speed of a local precipitation region based on a radar image without using the CC method, and also by accurately evaluating overall moving speed via a fluid equation, and PA0 (3) take topographical influences into prediction. PA0 (i) the pattern of the precipitation region is divided into one or more regions having a large edge-gradient and one or more regions having a small edge-gradient with respect to a predetermined value, and first initial advection vectors are determined by extracting a change of the center of gravity of each region having the large edge-gradient; PA0 (ii) second initial advection vectors are determined by dividing each frame into plural small blocks and calculating a direction and a distance relating to points having the highest similarity between two frames of the images based on the cross correlation method; PA0 (iii) third initial advection vectors are determined by extracting contours of the precipitation pattern in two of the images and assuming displacements between the contours as the advection vectors; and PA0 (1) A meteorological radar precipitation pattern prediction apparatus further comprising: image processing means for outputting area-transition information of a precipitation region with respect to two or more two-dimensional past images stored in the image storage means as one-dimensional time-series signals; function fitting means for fitting a non-linear function into the one-dimensional time-series signals by using the least square method; prediction means for predicting future area-transition based on results of the function fitting; and output means for outputting a pattern transition of the precipitation region as time-series images based on predicted results. (A method corresponding to this apparatus is also provided.) PA0 (2) A meteorological radar precipitation pattern prediction apparatus further comprising: image transition detecting means for detecting an intensity transition between two or more two-dimensional past images stored in the image storage means; image generating and vanishing means for generating or vanishing a local precipitation-region image according to the detected intensity transition by using an image processing method; and output means for outputting a pattern transition of the precipitation region as time-series images based on predicted results. Preferably, the image generating and vanishing means iterates convolution integral calculation and inverse integral calculation thereof with respect to a Gaussian function and image data of the precipitation region. PA0 (3) A meteorological radar precipitation pattern prediction apparatus further comprising: image processing means for detecting and outputting intensity and area transitions between two or more two-dimensional past images stored in the image storage means as one-dimensional time-series signals; precipitation-region growth and decay predicting means for predicting transition with respect to growth and decay of the precipitation region based on the one-dimensional time-series signals; and output means for outputting a pattern transition of the precipitation region as time-series images based on predicted results.
There is another problem in this case in which diffusion and advection effects are not considered together. That is, an actual transition, in which the precipitation pattern locally changes while both the wind speed and the amount of precipitation respectively and simultaneously change, cannot be predicted. Therefore, it is difficult to apply the conventional methods to a highly-unsteady precipitation pattern. In addition, advection velocities detected using the subblock matching method can be passably reliable; however, the advection velocity per pixel should be detected using another method.
On the other hand, prediction methods based on a neural network model are known, in which it has been tested to represent a mapping relationship between time-series-arranged two-dimensional images using weight coefficients of a neural network. However, the best suited structure of the neural network cannot be easily estimated and only a predicted image as an average of learned patterns can be obtained. More specifically, a feedforward network, one of representative time-series learning models, has the ability to map a spatial pattern, but a time-series pattern cannot be learned by using such a network (refer to "Brain and Neural Network" edited by S. Amari, et al., Asakura Publishing). That is, only prediction on conditions of fixed gray-levels and a fixed center of gravity for a precipitation pattern has been realized; thus, prediction of precipitation patterns using a neural network model cannot be put to practical use for the present.
Furthermore, precipitation patterns may be subjected to topographical influences of mountains, seas, and the like. However, in the prediction process using the linear extrapolation method, a measure such that different moving vectors are used for regions on the sea and the land can be taken at the best. Also in the neural network models, it is unclear how deeply topographical effects are considered, and moreover, flexibility of mathematical expressive-capability is insufficient regarding, for example, how a physical effect which is too complicated to learn is reflected in the model.